The realist interpretation's second-order claims about universal magnitudes introduce ontological commitments that restrict its application to domains where such universals are contentious.

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Second-order claims(in logic and metaphysics): Statements that talk *about* other statements or concepts, rather than directly describing things in the world—like saying 'the idea of beauty is complicated' rather than 'that painting is beautiful.'
contentious(describing Kvanvig's assumption): Debatable or disputed—something that philosophers genuinely disagree about rather than accept as obviously true.
ontological commitments(Quine's conception as applied to our best global theory): The demands that the truth of our total theory imposes on the world.
realist interpretation(in philosophy of science and quantum mechanics): The view that something exists and has properties independently of whether anyone is observing it or thinking about it.
universal magnitudes(Mundy and Swoyer's realist reinterpretation of measurement axioms): Universal properties instantiated by concrete objects, such as the universal property of being 5 meters long, as distinct from the concrete instantiations of that property
universals(Debated in Lefèvre's Disceptatio de universali between two students of Chrysippus's academy): Either what particular classes of things share, or what those who reason say they share (decided by convention)

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